Need a lot more info to be of help. What model is the computer, are you trying to connect using a wired connection or Wi-Fi. What is the router you have installed. Have you set up wireless security etc etc
Mobile phones connect to the internet via the mobile phone provider's network. Your daughter's laptop will connect to any available wireless network via its own inbuilt wireless adapter - it will recognise all available networks and offer them to her. She'll be able to connect to any of them, provided she knows the network password.
Your own wireless router will have a default password, and this is usually printed on a label that's on the underside of the router.